The term qubit (or qbit) stands for “quantum bit” which is a unit of quantum data. It is the quantum analogue of the term ‘bit’ used in classical computer architectures. A qubit has two states: vertical polarization and horizontal polarization. But quantum computing is different from classical digital computing in that these the two states can exist as a superposition of these two states and thus a qubit can contain more information than a classical digital bit.
Qubits come in many forms, including both atomic approaches such as single, laser-cooled ionized atoms in RF traps and solid-state approaches such as superconductor or semiconductor-based systems. The latter have more promise for scalability by leveraging large-scale fabrication methods from modern microelectronics, but typically require cryogenic operation. Superconducting qubits require cryogenics to maintain superconductivity; for semiconductor qubits, the reasons for cold operation are more subtle. In fact, room temperature coherence has been demonstrated for some semiconductor qubits, including nuclei in silicon (see Saeedi, Kamyar et al., “Room-Temperature Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon-28” Science 342 (6160) 2013), electrons and nuclei of defects in diamond (see M. V. G. Dutt et al., “Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond,” Science 316 (5829), 2007) or silicon carbide (W. F. Koehl et al., “Room temperature coherent control of defect spin qubits in silicon carbide,” Nature 479, 84 (2011)) and other systems. The key challenge of all these systems is the relative isolation and random placement of these types of qubits; forming well controlled, scalable arrays of these qubit types is extremely challenging. Of semiconductor qubits, those that are most naturally suited for the fabrication of scalable, deliberately placed arrays are electrically defined quantum dots. For background material regarding such dots, see, for example, R. Hanson et al., “Spins in few-electron quantum dots,” Reviews of Modern Physics 79, 1217 (2007). These use a combination of semiconductor interfaces and lithographically defined metal gates to trap electrons whose spins may be used as qubits. While these quantum dots more scalable from a fabrication point-of-view, electrically controlled quantum dot qubits operate at low temperature, typically beneath 1 K.
Quantum dots fully confine electrons in three dimensions. Typically, at least one dimension is confined by a semiconductor heterostructure or semiconductor-oxide interface, defined by epitaxy or deposition. The other two dimensions of confinement may then be provided by electrostatic gates or by other interfaces. For those dots using electrostatic gates, the rather weak confinement provided by the gates requires <1 K operation to avoid thermal excitation into low-lying orbital states. Fully semiconductor-defined dots such as self-assembled InAs quantum dots in GaAs are confined three dimensionally by the InAs-to-GaAs interface, and therefore have much larger confinement potentials and so may be operated at much higher temperatures (>10 K), but again these are difficult to scale into extensible arrays. Embodiments of the present invention relate to etched quantum dots, in which one or more of the confinement dimensions are provided by an etched semiconductor-to-vacuum interface (or semiconductor-to-insulator interface if encapsulated). Individual etched dots with high-temperature operation have been demonstrated as single-photon sources. See L. Zhang et al., “Charge-Tunable Indium Gallium Nitride Quantum Dots,” Physical Review B 93(8), 085301 (2016). The present applications considers the extension of such single etched dots into arrays enabling a controllable exchange coupling exists from one dot to the next. This controllable exchange coupling enables “quantum coherent logic,” as in more traditional exchange-based spin qubits.
In accordance with embodiments of the present invention, the essence of the controlled exchange coupling for etched dots is to define arrays of dots by a “nanopillar ridge.” This nanopillar ridge is etched following atomic planes, for example the “m-planes” of Wurtzite GaN. The pillar sidewalls provide transverse electron confinement while a quantum well, for example implemented as InGaN in GaN or GaN in AlGaN, provides vertical confinement within each pillar of the “nanopillar ridge”. The “nanopillar ridge” or simply “ridge” is not composed of isolated pillars or a smooth beam, but is preferably implemented in rather a corrugated pattern or structure in which transverse constrictions exist between neighboring dot locations in neighboring pillars. The size of those constrictions may be precisely controlled by etching the semiconductor materials and the size of those constrictions determines the rate of quantum tunneling from one Quantum Dot (QD) site in one pillar to the next QD site in the next (neighboring) pillar. To construct an array of qubits, quantum tunneling is combined with the detuning of the energy levels of dots via electrostatic metal gates at each dot site to establish voltage-controlled kinetic exchange. Qubit operation may be controlled via gate voltages, via laser-induced excitons in the the QDs (also sometimes called just ‘dots’ herein), or a combination thereof.
An important advantage of using etched interfaces for quantum dots is that they enable much higher temperature qubit operation relative to more traditional spin qubits. See R. Hanson, Phys. Rev. Lett. 91, 196802 (2003); J. R. Petta, et al. Science 309, 2180 (2005); H. Bluhm, et al. Nature Phys. 7, 109 (2011); M. D. Shulman, et al. Science 336, 202 (2012); M. D. Shulman, et al. Nature Comm. 5, 5156 (2014); B. M. Maune, et al. (HRL) Nature 481, 344 (2012); K. Eng, et al. (HRL) Science Advances 1, e1500214 (2015); and M. Veldhorst, et al. Nature 526, 410 (2015).
When surface etching defines quantum dots for spin qubits, the resulting dots may be very small (for “strongly confined” electrons) As a result, excited state energies are substantially higher than in more traditional exchange-based dots which use electrostatic gates for transverse confinement. In both etched and gated cases, a quantum well heterostructure provides strong vertical confinement. Excited state energies ultimately limit the temperature of operation, since high-fidelity qubit initialization depends on avoiding thermal excitation into excited states. As a comparison, traditional gated exchange-based spin qubits in the AlGaAs/GaAs (see the articles by R. Hanson, J. R. Petta, H. Bluhm, M. D. Shulman noted above), Si/SiO2 (see the article by M. Veldhorst noted above), or Si/SiGe (see the articles by B. M. Maune and K. Eng noted above) systems require dilution refrigerator temperatures, typically less than 1 K, due to excited state energies occurring at less than 1 meV. Etched dots, in contrast, may have excited state energies in excess of 7 meV, which enables operation at 77 K, the temperature of liquid nitrogen. Device operation using liquid nitrogen cryogenics or closed-cycle helium cryostats operating above 4 K are substantially less expensive and more tolerant of heat load than dilution refrigerators, giving substantial engineering importance to this temperature difference.
So “high temperature” in the context of this invention, means a temperature greater than 4 K, which, of course, is very cold relative to room temperature.
Note that this same principle of strong confinement underlies the higher temperature operation of spin qubits based on semiconductor defects (see F. Dolde, et al., Nature Phys. 9, 139 (2013)) or self-assembled quantum dots (see B. Sun, et al. Phys. Rev. Lett. 108, 187401 (2012); C. Schneider, et al. Nanotechnology 20, 434012 (2009); D. Kim, et al., Phys. Rev. Appl., 5, 024014 (2016)).
An advantage of etched dots relative to these other potentially high-temperature systems referenced in the preceding paragraph is that etched dots are fabricated on demand at prescribed locations, whereas self-assembly or defect implantation are random processes. The resulting random qubit placement of the prior art complicates fabrication and/or operation of arrays of qubits.
The notion that highly confined qubits allow higher temperature operation should be apparent to those skilled in this technology, but it is not obvious how to make existing highly confined qubits scalable to arrays larger than a few dots. The use of etched InGaN/GaN to make higher temperature single-spin qubits is known in the art (see L. Zhang, et al. Appl. Phys. Lett. 103, 192114 (2013) and L. Zhang, et al. Phys. Rev. B 93, 085301 (2016)), but the exchange coupling of multiple dots is not an obvious mode of operation. In the present invention, a novel geometry is disclosed which is based on etching to atomic planes of GaN crystal structure, which provides a controllable exchange coupling across an array of nanopillars. In most materials, the etched surface would destabilize the confined electron spins. In GaN, however, the low surface recombination velocity allows stable electrons close to the etched surfaces, making the presently disclosed techniques possible in a way unavailable to more traditional semiconductor systems such as Si or GaAs.